DOI QR코드

DOI QR Code

Design and ultimate behavior of RC plates and shells: two case studies

  • Min, Chang-Shik (Department of Civil and Environmental Engineering, Dongguk University)
  • 투고 : 2001.03.29
  • 심사 : 2002.05.18
  • 발행 : 2002.08.25

초록

Two cases of design are performed for the hyperbolic paraboloid saddle shell (Lin-Scordelis saddle shell) and the hyperbolic cooling tower (Grand Gulf cooling tower) to check the design strength against a consistent design load, therefore to verify the adequacy of the design algorithm. An iterative numerical computational algorithm is developed for combined membrane and flexural forces, which is based on equilibrium consideration for the limit state of reinforcement and cracked concrete. The design algorithm is implemented in a finite element analysis computer program developed by Mahmoud and Gupta. The amount of reinforcement is then determined at the center of each element by an elastic finite element analysis with the design ultimate load. Based on ultimate nonlinear analyses performed with designed saddle shell, the analytically calculated ultimate load exceeded the design ultimate load from 7% to 34% for analyses with various magnitude of tension stiffening. For the cooling tower problem the calculated ultimate load exceeded the design ultimate load from 26% to 63% with similar types of analyses. Since the effective tension stiffening would vary over the life of the shells due to environmental factors, a degree of uncertainty seems inevitable in calculating the actual failure load by means of numerical analysis. Even though the ultimate loads are strongly dependent on the tensile properties of concrete, the calculated ultimate loads are higher than the design ultimate loads for both design cases. For the cases designed, the design algorithm gives a lower bound on the design ultimate load with respect to the lower bound theorem. This shows the adequacy of the design algorithm developed, at least for the shells studied. The presented design algorithm for the combined membrane and flexural forces can be evolved as a general design method for reinforced concrete plates and shells through further studies involving the performance of multiple designs and the analyses of differing shell configurations.

키워드

참고문헌

  1. ACI 318-99. (1999), "Building code requirements for reinforced concrete and commentary (ACI 318R-99)", American Concrete Institute, P.O. Box 9094, Farmington Hills, MI 48333.
  2. ACI SP-110. (1988), "Hyperbolic paraboloid shells: state of the art", American Concrete Institute, Prepared by ACI Committee 334 - Joint ACI-ASCE, SP-110, 1988.
  3. ACI-ASCE. (1984), "Reinforced concrete cooling tower shells - practice and commentary", ACI J., Nov.-Dec. ACI-ASCE Comm. 334, Title No. 81-52.
  4. Akbar, H. and Gupta, A.K. (1985), "Membrane reinforcement in concrete shells: design versus nonlinear behavior", Reinf. Concrete Shell Res. Rep., North Carolina State Univ., Raleigh, NC 27695-7908.
  5. CEB-FIP Model Code. (1991), Comite Euro-International du Beton, Final Draft, Bull. d'Inform., 203, 204, 205.
  6. Chen, W.F. (1982), Plasticity in Reinforced Concrete, McGraw-Hill Book Company, 474 pp.
  7. Cheng, Y.M. (1995), "Finite element modeling of reinforced concrete structures with laboratory verification", Struct. Engrg. and Mech., 3(6), 593-609. https://doi.org/10.12989/sem.1995.3.6.593
  8. Cho, H.J. and Min, C.S. (2000), "Combined membrane and flexural reinforcement in plates and shells", J. Korean Society of Civil Engineers, 29(5-A), 725-735 (in Korean).
  9. Choi, C.-K. and Noh, H.-C. (2000), "Stochastic analysis of shape imperfection in RC cooling tower shells", J. Struct. Engrg., ASCE, 126(3), 417-423. https://doi.org/10.1061/(ASCE)0733-9445(2000)126:3(417)
  10. Gupta, A.K. (1978), "Grand gulf cooling tower study", Tech. Rep., IIT Res. Inst., Chicago, Illinois, Dec. Proj. J8325/Rep. No. 78J063.
  11. Gupta, A.K. (1984), "Membrane reinforcement in concrete shells: a review", Nuclear Engrg. Design, 82, 63-75. https://doi.org/10.1016/0029-5493(84)90267-X
  12. Gupta, A.K. (1986), "Combined membrane and flexural reinforcement in plates and shells", J. Struct. Div., ASCE, 112(3), 550-557. https://doi.org/10.1061/(ASCE)0733-9445(1986)112:3(550)
  13. Lourenco, P.B. and Figueiras, J.A. (1995), "Solution for the design of reinforcement concrete plates and shells", J. Struct. Engrg., ASCE, 121(5), 815-823. https://doi.org/10.1061/(ASCE)0733-9445(1995)121:5(815)
  14. Lin, C.S. and Scordelis, A.C. (1975), "Nonlinear analysis of RC shells of general form", J. Struct. Div., ASCE, 101(3), 523-538.
  15. Mahmoud, B.E.H. and Gupta, A.K. (1993), "Inelastic large displacement behavior and buckling of hyperbolic cooling tower shells", Tech. Rep., NCSU, Raleigh, NC.
  16. Mang, H.A., Floegl, H., Trappel, F. and Walter, H. (1983), "Wind-loaded reinforced-concrete cooling towers: buckling or ultimate load?", Engrg. Struct., 5, 163-180. https://doi.org/10.1016/0141-0296(83)90014-7
  17. Milford, R.V. and Schnobrich, W.C. (1984), "Nonlinear behavior of reinforced concrete cooling towers", Tech. Rep. Univ. of Illinois, Urbana-Champaign, IL 61801, Struct. Res. Series No. 514.
  18. Min, C.S. and Gupta, A.K. (1992), "A study of inelastic behavior of reinforced concrete shells using supercomputers", Tech. Rep., NCSU, Raleigh, NC.
  19. Min, C.S. and Gupta, A.K. (1993), "Inelastic behavior of hyperbolic cooling tower", J. Struct. Engrg., ASCE, 119(7), 2235-2255. https://doi.org/10.1061/(ASCE)0733-9445(1993)119:7(2235)
  20. Min, C.S. and Gupta, A.K. (1994), "Inelastic behavior of reinforced concrete hyperbolic paraboloid saddle shell", Engrg. Struct., 16(4), 227-237. https://doi.org/10.1016/0141-0296(94)90061-2
  21. Min, C.S. and Gupta, A.K. (1995), "Vector algorithm for layered reinforced concrete shell element stiffness matrix", Struct. Engrg. and Mech., 3(2), 172-183.
  22. Min, C.S. and Gupta, A.K. (1996), "Inelastic vector finite element analysis of RC shells", Struct. Engrg. and Mech., 4(2), 139-148. https://doi.org/10.12989/sem.1996.4.2.139
  23. Min, C.S. (1997a), "Ultimate behavior of RC hyperbolic paraboloid saddle shell", Struct. Engrg. and Mech., 5(5), 507-512. https://doi.org/10.12989/sem.1997.5.5.507
  24. Min, C.S. (1997b), "Design versus nonlinear behavior of RC hyperbolic paraboloid saddle shell", J. Korean Society of Civil Engineers, 17(I-6), 935-945 (in Korean).
  25. Min, C.S. (1999), "Design of RC plates and shells subjected to membrane force and flexural moment", J. Korean Society of Civil Engineers, 19(I-2), 171-183 (in Korean).
  26. Muller, G. and Scordelis, A.C. (1977), "Nonlinear analysis of reinforced concrete hyperbolic paraboloid shells", Tech. Rep., University of California, Berkeley, California 94720, October, Report No. UC-SESM 77-6.
  27. Noh, H.C. (1999), "Wind induced nonlinear behavior of reinforced concrete hyperbolic shell with shape imperfection", Ph.D. Thesis, Civil Engrg. Dept., Korea Advanced Institute of Science & Technology.
  28. Vecchio, F.J. (1998), "Lessons from the analysis of a 3-D concrete shear wall", Struct. Engrg. and Mech., 6(4), 439-455. https://doi.org/10.12989/sem.1998.6.4.439
  29. Zurn Ind. (1977), "Design blue lines and copies: shell reinforcing - tower 1 & 2", Grand Gulf Nuclear Station, Nov. Provided by private comm. from Zurn Balcke-Durr Ind., Inc., Tampa, FL.

피인용 문헌

  1. Rebar section loss and carbon fiber reinforced plastic reinforcement effects on nonlinear behavior and ultimate load of cooling towers vol.136, 2017, https://doi.org/10.1016/j.engstruct.2017.01.039
  2. Design and ultimate behavior of RC plates and shells vol.228, pp.1-3, 2004, https://doi.org/10.1016/j.nucengdes.2003.06.023
  3. Finite Element Analysis of Gabled Hyperbolic Paraboloid Shells vol.12, pp.1, 2012, https://doi.org/10.9712/KASS.2012.12.1.087